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International Summer School on Aggregation Operators

AGOP 2019: New Trends in Aggregation Theory pp 151–159Cite as

On Some Generalizations of the Choquet Integral

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

Abstract

In the present paper we survey several generalizations of the discrete Choquet integrals and we propose and study a new one. Our proposal is based on the Lovász extension formula, in which we replace the product operator by some binary function F obtaining a new n-ary function \(\mathfrak {I}^F_{m}\). We characterize all functions F yielding, for all capacities m, aggregation functions \(\mathfrak {I}^F_{m}\) with a priori given diagonal section.

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References

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Acknowledgments

This work was supported by the Slovak Research and Development Agency under the contract no. APVV-17-0066, grant VEGA 1/0682/16, grant VEGA 1/0614/18 and TIN2016-77356-P(AEI/FEDER,UE).

Author information

Authors and Affiliations

  1. Department of Statistics, Computer Science and Mathematics, Institute of Smart Cities, Universidad Pública de Navarra, Campus Arrosadía s/n, P.O. Box 31006, Pamplona, Spain

    Humberto Bustince & Javier Fernandez

  2. Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Radlinského 9, 812 37, Bratislava, Slovak Republic

    L’ubomíra Horanská

  3. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 810 05, Bratislava 1, Slovak Republic

    Radko Mesiar & Andrea Stupňanová

Authors
  1. Humberto Bustince
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  2. Javier Fernandez
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  3. L’ubomíra Horanská
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  4. Radko Mesiar
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  5. Andrea Stupňanová
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Corresponding author

Correspondence to L’ubomíra Horanská .

Editor information

Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

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Bustince, H., Fernandez, J., Horanská, L., Mesiar, R., Stupňanová, A. (2019). On Some Generalizations of the Choquet Integral. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_14

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